Comparison between Presidential and Parliamentary systems

In democratic systems of governance based on the trias politica, a fundamental parallel and a fundamental difference exists between presidential systems and constitutional monarchic parliamentary system of government.
The parallel is that the three branches of government (legislative, executive, judicial) exist largely independent of each other, with their own prerogatives, domains of activity, and exercises of control over each other.
The legislative body has control of the executive finances, and has judiciary powers, it also has control of the way the judiciary works.
The judiciary often has control of laws not being contradictory to the constitution or other laws and it has the power to correct and control the way the executive body exercises its powers (to execute the law)
The difference between the two systems is:
In presidential systems, the chief executive is elected to office and, after transfer of power, appoints his or her administration (like in the United States, with a unitary executive). However, a government headed by a prime minister is formed within the parliament, based on the elected majority (as in France, for example). The latter might lead to "cohabitation" where a president and his government belong to different parties or coalitions.
In constitutional monarchic parliamentary systems, only the legislative body is elected and a government formed on the basis of majority or a coalitions of parties. In syst ms modelled on the British system, elected members of the legislature who are appointed to executive positions retain their seats in the legislature. However in some other parliamentary systems, elected members of parliament have to resign from their mandate in order to accept an executive office. This is true in regional and local councils are elected and the executive nominated.
In some parliamentary systems, when the term of the legislature ends, so too may the tenure of the executive selected by that legislature. In other parliamentary systems, the executive stays in office until a new executive is appointed. However, in a presidential system, the executive's term may or may not coincide with the legislature's, as their selection is technically independent of the legislature.
Two-branch power systems may have systems in which certain branches have more than one power. Often a legislative body is elected, while the executive is nominated. The nominated executive branch also has power of presenting legislation, while the legislative body only has a controlling function. In those systems, the judiciary is subservient to the executive and has no power to control either the executive or the legality of new legislative texts.
The separation of powers is a doctrine which provides a separate authority that makes it possible for the authorities to check each other's checks and balances (see United States Executive Authority Act 1936).